RLDDM Model Comparison for CBB¶

as of 9/7/2021¶

Model 1: Symmetric Learning¶

This is a standard RLDDM model. The model assumes that participants update expected values between two doors according to a simple Rescorla-Wagner updating rule. Choices are made over these expected values according to a logistic softmax function, with a temperature parameter that reflects sensitivity to noise. Response times are assumed to be sampled from a Wiener first passage time distribution with parameters reflecting boundary separation (emphasis on speed or accuracy), the rate of evidence accumulation, initial bias, and non-decision time. The rate of evidence accumulation is assumed to be a weighted difference between expected values.

Parameters¶

alpha = boundary separation (as $\alpha \rightarrow \infty$, accuracy increases at the cost of speed; hesitancy)
beta = initial bias (should be around $0$ for no bias; $\beta > 0.5$ is bias toward the exploitative door)
deltac = drift rate scalar (as $\delta c \rightarrow \infty$, differences between expected values are more weighted as evidence for a decision)
tau = non-decision time (proportion of response time, in seconds, that does not reflect decision-making)
A = learning-rate (as $A \rightarrow 1$, updating is more reactive to reward prediction errors; larger swings)
B = inverse sensitivity to noise (as $B \rightarrow \infty$, choice becomes more deterministic or exploitative)

Model 2: Asymmetric Learning¶

This is identical to Model 1 except that it uses separate learning-rates for positive and negative feedback.

Additional Parameters¶

Ap = learning-rate to positive feedback
An = learning-rate to negative feedback

Model Comparison¶

Here we compare point-wise out-of-sample predictive accuracy between models (Vehtari et al., 2017). This is accomplished by computing leave-one-out cross-validation scores using Pareto smoothed importance sampling. Cross-validation scores reflect expected log point-wise predictive densities weighted with penalty terms controlling for both a model’s goodness of fit to the data and the complexity of the model.

Higher loo means better fit. Here, we see that the symmetric model better fits the data.

In [242]:
compdf = az.compare({'asymmetric': azdf1, 'symmetric': azdf2}, ic='loo')
compdf
Out[242]:
rank loo p_loo d_loo weight se dse warning loo_scale
symmetric 0 -668.754513 94.073852 0.0 NaN 818.34113 0.0 True log
asymmetric 1 -5005.142643 3179.161037 4336.38813 0.0 149.240192 895.248201 True log
In [239]:
az.plot_compare(compdf)
Out[239]:
<AxesSubplot:xlabel='Log'>

Symmetric Model: Parameter Correlations¶

Here, we check the correlation between parameters in the Happy, Sad, Angry, Desire, and Neutral conditions. Correlation between parameters posteriors can indicate interdependence during sampling. If we have interdependence, it can be difficult to make inferences about effects of condition. For example, a low learning-rate and high noise sensitivity in the Happy condition can lead to the same likelihood as a high learning-rate and low noise sensitivity in that same group; what we estimated could be happenstance.

What do we find?¶

We do find that some parameters are correlated, such as drift-rate scalar and noise sensitivity (which makes sense, considering that we'd expect a more exploitative person would be more likely to consider expected value differences as evidence). That said, we must be careful when making inferences about correlated parameters such as these. For example, if we estimate both of these parameters to be high in, say, the Happy group, it could be just as likely in reality that they are both low in that group, and our sampler simply converged on the high values by happenstance. We'll want to do more robust parameter recovery as a sanity check later. For now, we'll consider our parameter estimates accurate.

In [327]:
plot_paramcorr(df1, paramsearch(df1), ['Happy', 'Sad', 'Angry', 'Desire', 'Neutral'])

Asymmetric Model: Parameter Correlations¶

Let's run the same correlations for the Asymmetric Model.

What do we find?¶

The parameters are slightly less correlated, which is good for inference. We can also see now that the negative correlation between learning-rate and noise sensitivity in the Symmetric Model is mostly due to learning from positive feedback. Maybe people aren't learning much from negative feedback on this task?

In [328]:
plot_paramcorr(df2, paramsearch(df2), ['Happy', 'Sad', 'Angry', 'Desire', 'Neutral'])

Symmetric Model: Happy vs. Neutral¶

Alpha - Boundary Separation¶

Happy condition had a smaller boundary separation than Neutral condition. This suggests that people in the Happy condition focused more on speed than accuracy.

Beta - Initial Bias¶

Happy condition had an equivalent bias as Neutral condition.

Deltac - Drift-Rate Scalar¶

Happy condition had an equivalent weight of EV differences on drift-rate as Neutral condition.

Tau - Non-Decision Time¶

Happy condition had a shorter non-decision time than Neutral condition. This is about 45 milliseconds difference, so it's probably not meaningful.

A - Learning-Rate¶

Happy condition had a smaller learning-rate than Neutral condition.

B - Inverse Noise Sensitivity¶

Happy condition had an equivalent inverse noise sensitivity as Neutral condition.

In [337]:
bayeseffect(df1, 'alpha', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'beta', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'deltac', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'tau', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'A', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'B', 'Happy', 'Neutral', 0.8, 0.95)
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.016
H0 Odds: 0.32
H1 Odds: 1.035
There is 223.227% more evidence for the alternative hypothesis than the null for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 3.232
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.26
H0 Odds: 5.234
H1 Odds: 0.779
There is 571.869% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.149
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.167
H0 Odds: 3.366
H1 Odds: 0.877
There is 283.975% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.26
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.0
H0 Odds: 0.0
H1 Odds: 1.052
There is 95682789430.198% more evidence for the alternative hypothesis than the null for an effect at 0.8
Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8
BF: 956827895.302
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.007
H0 Odds: 0.144
H1 Odds: 1.045
There is 625.765% more evidence for the alternative hypothesis than the null for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 7.258
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.178
H0 Odds: 3.595
H1 Odds: 0.865
There is 315.777% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.241
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.

Symmetric Model: Sad vs. Neutral¶

Alpha - Boundary Separation¶

Sad condition had a slightly larger boundary separation than Neutral condition, but not enough to be considered significant. If this effect were greater, it would suggest that people in the Sad condition focused more on accuracy than speed.

Beta - Initial Bias¶

Sad condition had an equivalent bias as Neutral condition.

Deltac - Drift-Rate Scalar¶

Sad condition had a slightly larger weight of EV differences on drift-rate than Neutral condition, but not enough to be considered significant. If this effect were greater, it would suggest that people in the Sad condition used EV differences more as evidence.

Tau - Non-Decision Time¶

Sad condition had a shorter non-decision time than Neutral condition. This is about 25 milliseconds difference, so it's probably not meaningful.

A - Learning-Rate¶

Sad condition had a smaller learning-rate than Neutral condition.

B - Inverse Noise Sensitivity¶

Sad condition had a slightly larger inverse noise sensitivity than Neutral condition, but not enough to be considered significant. If this effect were greater, it would suggest that people in the Sad condition were more exploitative.

In [338]:
bayeseffect(df1, 'alpha', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'beta', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'deltac', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'tau', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'A', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'B', 'Sad', 'Neutral', 0.8, 0.95)
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.044
H0 Odds: 0.89
H1 Odds: 1.006
There is 12.979% more evidence for the alternative hypothesis than the null for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 1.13
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.254
H0 Odds: 5.126
H1 Odds: 0.785
There is 553.292% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.153
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.036
H0 Odds: 0.717
H1 Odds: 1.015
There is 41.537% more evidence for the alternative hypothesis than the null for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 1.415
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.0
H0 Odds: 0.0
H1 Odds: 1.052
There is 2539156.405% more evidence for the alternative hypothesis than the null for an effect at 0.8
Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8
BF: 25392.564
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.001
H0 Odds: 0.019
H1 Odds: 1.051
There is 5534.732% more evidence for the alternative hypothesis than the null for an effect at 0.8
Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8
BF: 56.347
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.084
H0 Odds: 1.695
H1 Odds: 0.964
There is 75.848% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.569
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.

Symmetric Model: Angry vs. Neutral¶

Alpha - Boundary Separation¶

Angry condition had a larger boundary separation than Neutral condition. This suggests that people in the Angry condition focused more on accuracy than speed.

Beta - Initial Bias¶

Angry condition had an equivalent bias as Neutral condition.

Deltac - Drift-Rate Scalar¶

Angry condition had an equivalent weight of EV differences on drift-rate as Neutral condition.

Tau - Non-Decision Time¶

Angry condition had an equivalent non-decision time as Neutral condition.

A - Learning-Rate¶

Angry condition had a smaller learning-rate than Neutral condition.

B - Inverse Noise Sensitivity¶

Angry condition had an equivalent inverse noise sensitivity as Neutral condition.

In [339]:
bayeseffect(df1, 'alpha', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'beta', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'deltac', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'tau', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'A', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'B', 'Angry', 'Neutral', 0.8, 0.95)
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.004
H0 Odds: 0.086
H1 Odds: 1.048
There is 1111.49% more evidence for the alternative hypothesis than the null for an effect at 0.8
Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8
BF: 12.115
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.265
H0 Odds: 5.335
H1 Odds: 0.774
There is 589.498% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.145
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.239
H0 Odds: 4.819
H1 Odds: 0.801
There is 501.899% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.166
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.154
H0 Odds: 3.109
H1 Odds: 0.89
There is 249.319% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.286
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.016
H0 Odds: 0.314
H1 Odds: 1.036
There is 230.207% more evidence for the alternative hypothesis than the null for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 3.302
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.23
H0 Odds: 4.626
H1 Odds: 0.811
There is 470.689% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.175
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.

Symmetric Model: Desire vs. Neutral¶

Alpha - Boundary Separation¶

Desire condition had a larger boundary separation than Neutral condition. This suggests that people in the Desire condition focused more on accuracy than speed.

Beta - Initial Bias¶

Desire condition had an equivalent bias as Neutral condition.

Deltac - Drift-Rate Scalar¶

Desire condition had an equivalent weight of EV differences on drift-rate as Neutral condition.

Tau - Non-Decision Time¶

Desire condition had a longer non-decision time than Neutral condition. This is about 40 milliseconds difference, so it's probably not meaningful.

A - Learning-Rate¶

Desire condition had an equivalent learning-rate as Neutral condition.

B - Inverse Noise Sensitivity¶

Desire condition had an equivalent inverse noise sensitivity as Neutral condition.

In [340]:
bayeseffect(df1, 'alpha', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'beta', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'deltac', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'tau', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'A', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'B', 'Desire', 'Neutral', 0.8, 0.95)
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.009
H0 Odds: 0.188
H1 Odds: 1.042
There is 455.242% more evidence for the alternative hypothesis than the null for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 5.552
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.296
H0 Odds: 5.968
H1 Odds: 0.741
There is 705.872% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.124
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.248
H0 Odds: 5.005
H1 Odds: 0.791
There is 532.738% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.158
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.0
H0 Odds: 0.0
H1 Odds: 1.052
There is 290185305.198% more evidence for the alternative hypothesis than the null for an effect at 0.8
Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8
BF: 2901854.052
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.198
H0 Odds: 3.996
H1 Odds: 0.844
There is 373.656% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.211
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.24
H0 Odds: 4.843
H1 Odds: 0.799
There is 505.819% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.165
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.

Asymmetric Model: Contrasts¶

Here, I will display all contrasts for the asymmetric model. Since it is not the winning model, I will not draw inferences from the contrasts, but will report those contrasts for completeness. Recall that Ap is the learning-rate for positive feedback and An is for negative feedback.

In [341]:
bayeseffect(df2, 'alpha', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'beta', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'deltac', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'tau', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'Ap', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'An', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'B', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'alpha', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'beta', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'deltac', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'tau', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'Ap', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'An', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'B', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'alpha', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'beta', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'deltac', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'tau', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'Ap', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'An', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'B', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'alpha', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'beta', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'deltac', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'tau', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'Ap', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'An', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'B', 'Desire', 'Neutral', 0.8, 0.95)
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.01
H0 Odds: 0.205
H1 Odds: 1.041
There is 407.035% more evidence for the alternative hypothesis than the null for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 5.07
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.219
H0 Odds: 4.406
H1 Odds: 0.822
There is 435.865% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.187
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.169
H0 Odds: 3.404
H1 Odds: 0.875
There is 289.211% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.257
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.0
H0 Odds: 0.0
H1 Odds: 1.052
There is 1091642010.626% more evidence for the alternative hypothesis than the null for an effect at 0.8
Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8
BF: 10916421.106
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.012
H0 Odds: 0.248
H1 Odds: 1.039
There is 318.262% more evidence for the alternative hypothesis than the null for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 4.183
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.054
H0 Odds: 1.092
H1 Odds: 0.995
There is 9.729% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.911
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.152
H0 Odds: 3.07
H1 Odds: 0.892
There is 244.181% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.291
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.026
H0 Odds: 0.533
H1 Odds: 1.024
There is 92.167% more evidence for the alternative hypothesis than the null for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 1.922
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.188
H0 Odds: 3.786
H1 Odds: 0.855
There is 342.967% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.226
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.026
H0 Odds: 0.523
H1 Odds: 1.025
There is 95.898% more evidence for the alternative hypothesis than the null for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 1.959
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.0
H0 Odds: 0.0
H1 Odds: 1.052
There is 1469043.763% more evidence for the alternative hypothesis than the null for an effect at 0.8
Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8
BF: 14691.438
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.031
H0 Odds: 0.626
H1 Odds: 1.02
There is 62.755% more evidence for the alternative hypothesis than the null for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 1.628
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.001
H0 Odds: 0.028
H1 Odds: 1.051
There is 3631.519% more evidence for the alternative hypothesis than the null for an effect at 0.8
Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8
BF: 37.315
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.061
H0 Odds: 1.235
H1 Odds: 0.988
There is 25.055% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.8
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.004
H0 Odds: 0.076
H1 Odds: 1.048
There is 1272.845% more evidence for the alternative hypothesis than the null for an effect at 0.8
Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8
BF: 13.728
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.284
H0 Odds: 5.732
H1 Odds: 0.753
There is 661.184% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.131
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.221
H0 Odds: 4.458
H1 Odds: 0.819
There is 443.97% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.184
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.162
H0 Odds: 3.263
H1 Odds: 0.882
There is 270.012% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.27
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.013
H0 Odds: 0.263
H1 Odds: 1.038
There is 295.569% more evidence for the alternative hypothesis than the null for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 3.956
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.033
H0 Odds: 0.664
H1 Odds: 1.018
There is 53.231% more evidence for the alternative hypothesis than the null for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 1.532
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.213
H0 Odds: 4.295
H1 Odds: 0.828
There is 418.723% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.193
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.003
H0 Odds: 0.059
H1 Odds: 1.049
There is 1667.51% more evidence for the alternative hypothesis than the null for an effect at 0.8
Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8
BF: 17.675
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.301
H0 Odds: 6.064
H1 Odds: 0.736
There is 724.397% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.121
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.259
H0 Odds: 5.223
H1 Odds: 0.78
There is 569.945% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.149
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.0
H0 Odds: 0.0
H1 Odds: 1.052
There is 332936956.811% more evidence for the alternative hypothesis than the null for an effect at 0.8
Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8
BF: 3329370.568
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.177
H0 Odds: 3.567
H1 Odds: 0.866
There is 311.866% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.243
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.042
H0 Odds: 0.845
H1 Odds: 1.008
There is 19.357% more evidence for the alternative hypothesis than the null for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 1.194
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05
Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.266
H0 Odds: 5.362
H1 Odds: 0.772
There is 594.344% more evidence for the null hypothesis than the alternative for an effect at 0.8
FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1)
BF: 0.144
NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.